Abstract

We investigate the elasticity of an isolated, threefold junction of soap films (Plateau border), which displays static undulations when liquid rapidly flows into it. By analyzing the shape of the Plateau border (thickness R and transverse displacement) as a function of the liquidflow rate Q, we show experimentally and theoretically that the elasticity of the Plateau border is dominated by the bending of the soap films pulling on the Plateau border. In this asymptotic regime, the undulation wavelength obeys the scaling law ∼Q2R−2 and the decay length ∼Q2R−4.

We thank W. Drenckhan and C. Derec for enlightening discussions and criticisms and careful reading of the article. We also thank the referees of this article for their helpful comments. F.E. thanks the French Agence Nationale de la Recherche (Project No. SAMOUSSE ANR-11-BS09-001) for partial financial support.

Article outline:I. INTRODUCTIONII. EXPERIMENTAL SETUPIII. THEORY: FORMULATION OF THE PROBLEMA. One dimensional modelB. Derivation of the elastic restoring forceIV. DRAINAGE OF THE PLATEAU BORDERA. Model: Projection along the tangential vectorB. Measurement of the size of the Plateau borderC. Comparison between the model and the dataV. PLATEAU BORDER DEFORMATIONA. Model: Projection along the normal vectorB. Experimental measurement of the deformationC. Comparison between the model and the data1. x1(z): Relaxation of the central line2. Solution x2(z): Plateau border damped undulationsVI. DISCUSSION AND CONCLUSION